搜索圆环上不协作不对抗的变速目标算法

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中图分类号：TP301.6 文献标志码：A 文章编号：1001-3695（2025）10-020-3053-08

doi： 10. 19734/j. issn. 1001-3695. 2025.03.0073

Searching for non-adversarial， uncooperative target with non-constant speed on cycle

Wu Haonan，Wei ，Zhang Ruiyue，Li He （SchoolofComputerScience&ArtificialIntellgence，LiaoningNormal University，DalianLiaoning116o81，China）

Abstract：Searchingforatargetinaknownenvironmentisoneof thebasictasksof therobot，related problems have eceived muchatentionintheresearchofcomputational geometryandrobotics.The targetsearchproblemrequires therobottoadoptan efficient strategy to minimize the time to find the target. Assuming that k robots with maximum speed 1 are placed on a unit circle.Anon-adversarial，uncooperativetargetmovesalongthecirclewithvariablespeed.Thetaskoftherobotistosearch for thetarget.Searchalgorithmsweredevelopedacordingtothenumberofrobotsandtheknowledgeofthetarget，suchasthedirectionof movementand thespeedfunction.Forthesingle-robotcase，thispapercombined withthecharacteristicsof the modelandused visualizationdiagramtostudythetrajectories oftherobotand thetarget duringthesearchprocess.Byanalyzing thegeneralrequirementsthatthealgorithmshouldsatisfyundervariousconditions，itprovedtheoptimalityoftheproposedalgorithm，andotainedthecorrspondingupperandlowerboundswithrespectothespeed functionofthetarget.Further，it extended these results to the case of k⩾2 ，and proved the corresponding upper and lower bounds. Finally，，this paper verified the correctness of the theoretical analysis through simulation experiments.

Key words：computational geometry；path planning；searching；mobile robots

0 引言

机器人在特定区域内进行目标搜索是一个多学科交叉的研究问题，涉及数学、计算机科学、机器人学以及运筹学等。（剩余19072字）